Help:
The Member parameter specifies the recipient (mail-enabled object) that you want to add to the group. You can use any value that uniquely identifies the recipient.
you can add existing contacts to distribution list, not just email address, so create contact and add it
Have you created the contact for the person that you are adding to a distribution group?
You will have to create a contact (or mail user) if the person has an external email.
Then add it to the Distribution List?
e.g
I see. It looks like you already have the Contact created.
If you have Office 365 AD connect/DirSync running and all your on-premise AD synchronises to Office365 or Azure AD, then you can easily add the Contact (AD object) into the Distribution Group (again AD object) on your local ActiveDirectory Users and Computers. This will then sync across office 365.
Or, if you manage all your Contact/MailUser and Distribution Group on the office 365 then try
Get-MailContact -Identity “Chris Ashton” | Format-List
If it returns the right value then you should be able to Add-DistributionGroupMember
If this still fails, I will submit a support request on office 365 portal.
Hope this helps!